Logistic Regression Model

A mixed logistic regression model was developed to test associations between independent variables and the dependent variable, owner-reported provision of uncontrolled outdoor access. Country and province/state were included as random effects. Referent categories for categorical variables were chosen based on biological plausibility or based on the most common response. Correlation analysis was performed on all retained variables, with a correlation coefficient of >|0.7| suggesting collinearity (33). Five correlations related to owner perspectives of outdoor access were detected during this assessment (perspective of access providing natural hunting behavior, natural environment, risk of obesity, natural exploratory behavior, and physical activity), and the most biologically meaningful variables that captured the most information were retained for further analysis (natural hunting behavior, natural environment, and physical activity) (33). Linear relationships between continuous independent variables and the outcome variable (uncontrolled outdoor access) were visually assessed using locally weighted regression curves (lowess) and quadratic relationships were assessed by testing the significance of a quadratic term. If the relationship was quadratic, the quadratic term was retained in the model. If the relationship was neither non-linear nor quadratic, the continuous variable was categorized. As a result of non-linear associations, the following variables were categorized based on biological/practical cut-points: participant age (18–24, 25–44, 45–64, 65+), time spent playing with the cats per day (<1, 1, 2, 3–12 h), and the number of cats owned (1, 2, 3+). Also, cat age was categorized based on the cat life stages presented in the AAFP 2010 guidelines (<4 months, 4–12 months, 1–6 years, 7–10 years, 11–14 years, and >15 years) (34).

Univariable analysis was performed to test each independent variable against the outcome, uncontrolled outdoor access. Variables were retained using a liberal p-value of p ≤ 0.20 (35). The final main effects model was built using forward stepwise selection method, where significant variables (p < 0.05) were retained in the final model. Two-way interactions between biologically plausible variables were tested. Confounders were tested based on their biological plausible relationship with an explanatory variable and the outcome. They were identified as a variable that caused >20% change in a coefficient of another variable in the model. Standardized Pearson residuals were used to detect outliers. The fit of the model was determined by assessing the homoscedasticity and normality of the best linear unbiased predictions (BLUPS). Also, the intra-class correlation coefficients (ICC) were estimated to measure the degree of correlation between cats owned within the same country and province/state.